Fig.1 Dynamical evolution of geometric quantum discord in a non-Markov hybrid bath and non-Markov single bath with X-direction KSEA interaction (a) the initial states $|\psi\rangle=(|00\rangle-|11\rangle) / \sqrt{2}$ and (b) |φ〉= 10〉, kA=kB=1, Jx=0.2, Jy=0.4, Jz=0.9, γ=0.7, Dx=0.4, Γx=0.8

Fig.2 Effects of KSEA interactions on dynamics of geometric quantum discord in (a) hybird non-Markov and (b) single non-Markov environments，the initial state $|\psi\rangle=(|00\rangle-|11\rangle) / \sqrt{2}$，kA=kB=1，Jx=0.2，Jy=0.4，Jz=0.9，γ=0.7，Dx=0.4

Fig.3 (a) 3-D projection diagram and (b) 3-D diagram of geometric quantum discord with time and KSEA interaction in hybird non-Markov environment, the initial state $|\psi\rangle=(|00\rangle-|11\rangle) / \sqrt{2}$; (c) effect of KSEA interactions on geometric quantum discord in hybird non-Markov environments at ωt=5, the initial state |φ〉= 10〉, Jx=0.2, Jy=0.4, Jz=0.9, γ=0.7, Dx=0.4

Fig.4 Dynamics of geometric quantum discord under (a) Markov hybrid bath and (b) Markov single bath with KSEA interaction, the initial state $|\psi\rangle=(|00\rangle-|11\rangle) / \sqrt{2}$, kA=kB=1, Jx=0.2, Jy=0.4, Jz=0.9, γ=3, Dx=0.4